# Questions tagged [copula]

A copula is a multivariate cumulative distribution function for which the marginal probability distribution of each variable is uniform on the unit interval.

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### What is the probability of $\alpha$- quantile

I didn't understand why the $P(X \leq q_{\alpha}^- (X))=\alpha$ for $0<\alpha<1$. Please help me with this. The setup for it: X is a real random variable and the lower $\alpha$-quantile defined ...
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### Variable change in Copula for the joint pdf of correlated random variables

Let $f_{X,Y}(x,y)$ be the joint probability density of correlated random variables $X$ and $Y$ based on a Copula $C$ (Gaussian in my case) where $f_X(x)$ and $f_Y(y)$ are the marginal probability ...
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### How to compare the entropy of copulas?

Three different bivariate copulas are shown below with increasing degrees of dependence (parameter $\theta$). Differential entropy is a measure of disorder in a probability density like the copula. ...
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### Impact of copula choice on quantiles (sum of random variables)

I am trying to get my head around the impact of different dependence structures (copulas) on the risk (quantiles) of a sum of dependent random variables (with arbitrary marginals). In a multivariate ...
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Most statistical measures are non-negative. Shannon entropy, $H(X)$, a statistical measure of disorder or uncertainty in probability distributions, is also non-negative, despite it having a negative ...